In this work, a new combined feature is proposed to improve the recognition of non-stationary acoustic sources. The idea is to overcome the non-stationarity problem on classification tasks due to mismatches that arise from natural statistics variations. The Index of Non-Stationarity (INS) is adopted to assess the non-stationarity behavior of acoustic signals on a frame-byframe basis, generating a new feature vector. The evaluation is performed with the combined MFCC+INS feature. Eight sources with different degrees of non-stationarity are selected for the acoustic source classification task. Experiments demonstrated that the proposed solution outperforms the baseline systems for the majority of individual acoustic sources, leading to significant increment in the average accuracy in all scenarios. Moreover, a single INS feature value is sufficient to obtain up to 2.7 percentage points gain on the average classification accuracy when compared to the baseline approach.